Sums involving generalized harmonic and Daehee numbers

Neşe Ömür and Sibel Koparal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 92—99
DOI: 10.7546/nntdm.2022.28.1.92-99
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Authors and affiliations

Neşe Ömür
Department of Mathematics, University of Kocaeli
41380 Izmit, Kocaeli, Turkey

Sibel Koparal
Department of Mathematics, University of Bursa Uludağ
16059 Nilüfer, Bursa, Turkey

Abstract

In this paper, we establish some sums involving generalized harmonic and Daehee numbers which are derived from the generating functions. For example, for n, r\geq 1,

    \begin{eqnarray*} \sum_{i=0}^{n}H\left( i,r-1,\alpha \right) H_{n-i}^{r}\left( \alpha \right) &=&\sum_{l_{1}+l_{2}+ \cdots +l_{r+1}=n}H_{l_{1}}(\alpha )H_{l_{2}}(\alpha ) \cdots H_{l_{r+1}}(\alpha ). \end{eqnarray*}

Keywords

  • Sums
  • Generalized harmonic numbers
  • Daehee numbers

2020 Mathematics Subject Classification

  • 05A15
  • 05A19
  • 11B73

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Manuscript history

  • Received: 24 January 2021
  • Revised: 11 February 2021
  • Accepted: 16 February 2022
  • Online First: 17 February 2022

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Cite this paper

Ömür, N., & Koparal, S. (2022). Sums involving generalized harmonic and Daehee numbers. Notes on Number Theory and Discrete Mathematics, 28(1), 92-99, DOI: 10.7546/nntdm.2022.28.1.92-99.

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